A new robust algorithm analyzing the geometry and connectivity of the pore space of sedimentary rock is based on fundamental concepts of mathematical morphology. The algorithm distinguishes between the ‘‘pore bodies’’ and ‘‘pore throats,’’ and establishes their respective volumes and connectivity. The proposed algorithm also produces a stick-and-ball diagram of the rock pore space. The tests on...

Abstract We show that, for every set of $n$ points in the $d$-dimensional unit cube, there is an empty axis-parallel box volume at least $\Omega (d/n)$ as $n\to \infty $ and $d$ fixed. In opposite direction, we give a construction without $O(d^2\log d/n)$. These improve on previous best bounds (\log d/n)$ $O(2^{7d}/n)$, respectively.

We show that in d-dimensional Euclidean space the maximum number of non-overlapping translates of a d-dimensional convex body K that can touch K and can lie in a closed supporting half-space of K is always at most 2 ·3d−1−1, with this bound to be reached only if K is an affine image of a d-cube. Such onesided Hadwiger configurations occur at the boundary of finite packings or near the holes in ...

Each packing of R d by translates of the unit cube [0, 1) d admits a decomposition into at most two parts such that if a translate of the unit cube is covered by one of them, then it also belongs to such a part. Let I = [0, 1) d , and S ⊂ R d be a non-empty set. We say that the set I + S = {I + s : s ∈ S} is a packing of R d by (half-open) unit cubes if the members of I + S are pairwise disjoin...

Introduction One possible way to express that the cube Q d = [0, 1] d has dimension d is to notice that it cannot be colored in d colors with arbitrarily small connected monochromatic components. A more precise statement was proved by Lebesgue: If the unit cube Q d is covered by closed sets with multiplicity at most d then one covering set must meet two opposite facets of Q d. An analogue of Gr...

We show that the minimal discrepancy of a point set in d-dimensional unit cube with respect to BMO seminorm suffers from curse dimensionality.

Wellbore instability is a quite common event during drilling, and causes many problems such as stuck pipe and lost circulation. It is primarily due to the inadequate understanding of the rock properties, pore pressure, and earth stress environment prior to well construction. This study aims to use the existing relevant logs, drilling, and other data from offset wells to construct a precise mech...

Scaffolds encourage the new tissue formation through biological substitution of damaged or lost tissues. Therefore, scaffold characteristics become more important and should be precisely controlled. Production scaffolds using a three dimensional (3d) printer appears as promising method in terms enabling homogeneous pore distribution uniform size arrangement. In this study, polylactic acid (PLA)...